1 Variable Distributions

The Concord Water Study

Mean, Variance, and Standard Deviation

Normal Distributions

Median and Interquartile Range

Boxplots

Symmetry Plots

Quantile Plots

Quantile–Quantile Plots

Quantile–Normal Plots

Power Transformations

Selecting an Appropriate Power

Conclusion

Exercises

Notes

2 Bivariate Regression Analysis

The Basic Linear Model

Ordinary Least Squares

Scatterplots and Regression

Predicted Values and Residuals

*R*^{2}, Correlation, and Standardized Regression Coefficients

Reading Computer Output

Hypothesis Tests for Regression Coefficients

Confidence Intervals

Regression Through the Origin

Problems with Regression

Residual Analysis

Power Transformations in Regression

Understanding Curvilinear Regression

Conclusion

Exercises

Notes

3 Basics of Multiple Regression

Multiple Regression Models

A Three-Variable Example

Partial Effects

Variable Selection

A Seven-Variable Example

Standardized Regression Coefficients

*t*-Tests and Confidence Intervals for Individual Coefficients

*F*-Tests for Sets of Coefficients

Multicollinearity

Search Strategies

Interaction Effects

Intercept Dummy Variables

Slope Dummy Variables

Oneway Analysis of Variance

Twoway Analysis of Variance

Conclusion

Exercises

Notes

4 Regression Criticism

Assumptions of Ordinary Least Squares

Correlation and Scatterplot Matrices

Residual Versus Predicted *Y* Plots

Autocorrelation

Nonnormality

Influence Analysis

More Case Statistics

Symptoms of Multicollinearity

Conclusion

Exercises

Notes

5 Fitting curves

Exploratory Band Regression

Regression with Transformed Variables

Curvilinear Regression Models

Choosing Transformations

Evaluating Consequences of Transformation

Conditional Effect Plots

Comparing Effects

Nonlinear Models

Estimating Nonlinear Models

Interpretation

Conclusion

Exercises

Notes

6 Robust regression

A Two-Variable Example

Goals of Robust Estimation

*M*-Estimation and Iteratively Reweighted Least Squares

Calculation by IRLS

Standard Errors and Tests for *M*-Estimates

Using Robust Estimation

A Robust Multiple Regression

Bounded-Influence Regression

Conclusion

Exercises

Notes

7 Logit regression

Limitations of Linear Regression

The Logit Regression Model

Estimation

Hypothesis Tests and Confidence Intervals

Interpretation

Statistical Problems

Influence Statistics for Logit Regression

Diagnostic Graphs

Conclusion

Exercises

Notes

8 Principal Components and Factor Analysis

Introduction to Components and Factor Analysis

A Principal Components Analysis

How Many Components?

Rotation

Factor Scores

Graphical Applications: Detecting Outliers and Clusters

Principal Factor Analysis

An Example of Principal Factor Analysis

Maximum-Likelihood Factor Analysis

Conclusion

Exercises

Notes

Appendix 1 Population and sampling distributions

Expected Values

Covariance

Variance

Further Definitions

Properties of Sampling Distributions

Ordinary Least Squares

Some Theoretical Distributions

Exercises

Notes

Appendix 2 Computer-Intensive Methods

Monte Carlo Simulation

Bootstrap Methods

Bootstrap Distributions

Residual Versus Data Resampling

Bootstrap Confidence Intervals

Evaluating Confidence Intervals

Computer-Intensive Methods in Research

Exercises

Notes

Appendix 3 Matrix Algebra

Basic Ideas

Matrix Addition and Multiplication

Regression in Matrix Form

An Example

Regression from Correlation Matrices

Further Definitions

Exercises

Notes

Appendix 4 Statistical tables

A4.1: Critical Values for Student’s *t*-Distribution

A4.2: Critical Values for the *F*-Distribution

A4.3: Critical Values for the Chi-Square Distribution

A4.4: Critical Values for the Durbin–Watson Test for Autocorrelation

References

Index